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The graph of the sine curve below is of electromagnetic energy that represents red light:

sine graph with points at 0, 0 and 160, 1 and 320, 0 and 480, negative 1 and 640, 0

What function accurately represents the sine curve for red light?

a) f(x) = sin pi over 640x
b) f(x) = sin 640πx
c) f(x) = sin 320πx
d) f(x) = sin pi over 320x

Respuesta :

Matheng
The general form of sine curve is   f(x) = a sin (nx)
Where: a is the amplitude and n = 2π/period

Given the points of the sine curve which is 
(0, 0) and (160, 1) and (320, 0) and (480, -1) and (640, 0)

the maximum value of f(x) = 1 , and the minimum value of f(x) = -1
∴ amplitude = a =1

And the function complates one cycle from 0 to 640
∴ period = 640  ⇒⇒⇒ n = 2π/640 = π/320

∴ f(x) = 1 * sin (π/320)x = sin (π/320)x

∴ The correct answer is option d
d) f(x) = sin pi over 320x


smmwaite
For the trigonometric graph, the functions is given by the general equation,

KSin(bx+Ф),
Where K ⇒Amplitude
            b =2π/Period and 
            Ф ⇒phase angle.

So, from our graph, the period is (320×2)=640°
∴b = 2π/640
      =π/320
The Amplitude of our graph is 1 and the phase angle is 0.
The function of this graph is;

f(x) = sin (π/320)x

The answer is d) f(x) = sin pi over 320x

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